Video Lectures

I will describe the main ideas that go into the proof of the (unramified, global) geometric Langlands conjecture. All of this work is joint with Gaitsgory and some parts are joint with Arinkin, Beraldo, Chen, Faergeman, Lin, and Rozenblyum. I will...

I will discuss a recent proof of new cases of the Hilbert-Smith conjecture for actions by homeomorphisms of symplectic nature. In particular, it rules out faithful actions of the additive p-adic group in this setting and provides further...

In this talk, we will present a new approach for approximating large independent sets when the input graph is a one-sided expander—that is, the uniform random walk matrix of the graph has second eigenvalue bounded away from 1. Specifically, we show...

In this talk, we will consider a stabilized version of the fundamental existence problem of symplectic structures (cf. Open Problem 1 in McDuff & Salamon). Given a formal symplectic manifold, i.e. a closed manifold M

with a non-degenerate 2-form and...

While the vast majority of the light from our galaxy comes from the Galactic disk, the vast majority of the mass of the Milky Way (MW) is in its dark matter halo. Because we cannot directly observe the MW's dark matter halo, we must use luminous...

A cornerstone result in geometry is the Szemerédi–Trotter theorem, which gives a sharp bound on the maximum number of incidences between m points and n lines in the real plane. A natural generalization of this is to consider point-hyperplane...

Triangulated surfaces are Riemann surfaces formed by gluing together equilateral triangles. They are also the Riemann surfaces defined over the algebraic numbers. Brooks, Makover, Mirzakhani and many others proved results about the geometric...

In this talk, I will discuss lower bounds for a certain set-multilinear restriction of algebraic branching programs. The significance of the lower bound and the model is underscored by the recent work of Bhargav, Dwivedi, and Saxena (2023), which...

In this talk I will discuss holographic duals of topological operators.  At low energy sugra, they can be realized by Page charge associated to Gauss law constraints. In the UV string theory, topological operators can be characterized by various...

Recent observations reveal that cosmic rays (CRs) are more tightly confined in various astrophysical systems (e.g. radio bubbles) than current theories predict. I show that microscale magnetic fluctuations, particularly from the mirror instability...